In papers by Arnold, Falk, and Winther, and by Hiptmair, novel multigrid methods for discrete -elliptic boundary value problems have been proposed. Such problems frequently occur in computational electromagnetism, particularly in the context of eddy current simulation.
This paper focuses on the analysis of those nodal multilevel decompositions of the spaces of edge finite elements that form the foundation of the multigrid methods. It provides a significant extension of the existing theory to the case of locally vanishing coefficients and nonconvex domains. In particular, asymptotically uniform convergence of the multigrid method with respect to the number of refinement levels can be established under assumptions that are satisfied in realistic settings for eddy current problems.
The principal idea is to use approximate Helmholtz-decompositions of the function space into an -regular subspace and gradients. The main results of standard multilevel theory for -elliptic problems can then be applied to both subspaces. This yields preliminary decompositions still outside the edge element spaces. Judicious alterations can cure this.
In this paper, a class of sextic Z7-equivariant Hamiltonian system is considered. Using the methods of qualitative analysis, bifurcations of the above system are analyzed, the phase portraits of the system are classified and representative orbits are shown by Maple software. 相似文献
NMR spectra of (14)N (spin I=1) are obtained by indirect detection in powders spinning at the magic angle. The method relies on the transfer of coherence from a neighboring "spy" nucleus with S=1/2, such as (13)C or (1)H, to single- or double-quantum transitions of (14)N nuclei. The transfer of coherence can occur through a combination of scalar and residual dipolar splittings (RDS); the latter are also known as second-order quadrupole-dipole cross terms. The two-dimensional NMR spectra reveal powder patterns determined by second- and third-order quadrupolar couplings. These spectra depend on the quadrupolar coupling constant C(Q) (typically a few megahertz), on the asymmetry parameter eta(Q) of the (14)N nucleus, and on the orientation of the internuclear vector r(IS) between the I ((14)N) and S (spy) nuclei with respect to the quadrupolar tensor. These parameters, which can be subject to motional averaging, can reveal valuable information about the structure and dynamics of nitrogen-containing solids. Application of this technique to various amino acids, either enriched in (13)C or with natural carbon isotope abundance, with spectra recorded at various magnetic fields, illustrates the scope of the method. 相似文献
We consider H(curl, Ω)-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by successive local mesh refinement, either by local uniform refinement with hanging nodes or bisection refinement. In this setting we develop a convergence theory for the the so-called local multigrid correction scheme with hybrid smoothing. We establish that its convergence rate is uniform with respect to the number of refinement steps. The proof relies on corresponding results for local multigrid in a H^1 (Ω)-context along with local discrete Helmholtz-type decompositions of the edge element space. 相似文献
The problem of deleting a row from a Q–R factorization (called downdating) using Gram–Schmidt orthogonalization is intimately
connected to using classical iterative methods to solve a least squares problem with the orthogonal factor as the coefficient
matrix. Past approaches to downdating have focused upon accurate computation of the residual of that least squares problem,
then finding a unit vector in the direction of the residual that becomes a new column for the orthogonal factor. It is also
important to compute the solution vector of the related least squares problem accurately, as that vector must be used in the
downdating process to maintain good backward error in the new factorization. Using this observation, new algorithms are proposed.
One of the new algorithms proposed is a modification of one due to Yoo and Park [BIT, 36:161–181, 1996]. That algorithm is
shown to be a Gram–Schmidt procedure.
Also presented are new results that bound the loss of orthogonality after downdating. An error analysis shows that the proposed
algorithms’ behavior in floating point arithmetic is close to their behavior in exact arithmetic. Experiments show that the
changes proposed in this paper can have a dramatic impact upon the accuracy of the downdated Q–R decomposition.
AMS subject classification (2000) 65F20, 65F25 相似文献
We examine the consequences of a variable (density-dependent) bag pressure term and a fixed hadronic size in the phenomenological
MIT bag model for hadron spectroscopy. Mass spectrum of the low-lying baryons and mesons, baryon magnetic moments and the
hadron mass splittings are estimated. These are found to be in closer agreement with experiment than the MIT results. 相似文献
Calculations of 119Sn electric field gradients (EFG) have been performed using the Extended Hückel approximation on characteristic molecular clusters simulating possible types of sites in chalcogenide glasses. The motivation for these calculations derives from theoretical concepts on varying near neighbor relationships in these types of glasses, and from recent 119Sn Mössbauer experiments on Sn-doped Gex(Se or S)1–x bulk glasses which reveal three types (A, B and C) of chemically inequivalent sites, with distinct values and composition dependences for their isomer shifts and quadrupole splittings. The model clusters chosen for the calculations were the ethane-like (Ge2Se3)n quasi-one-dimensional chains of varying lengths which have been proposed as possible sources of the B site. In addition, calculations were also carried out on several additional types of clusters, in order to help in interpreting the results for the chains. We find that the magnitude of the quadrupole splitting in isolated linear ethane-like chains is very small, and almost independent of the particular site along the chain at which Sn replaces Ge. It therefore seems unlikely that such isolated linear clusters would be the source of the B sites. These sites are more likely to be related to distortions of the ethane-like clusters into non-linear configurations, as well as interactions with neighboring clusters, as forced by the constraints of the packing in the structure of the glass. 相似文献